The full, formally correct version (at least in British English) would be:

"I have never been bitten by a shark."

"I was never bitten by a shark" is an abbreviated form that you may hear in conversational English. To me, the use of "bit" for "bitten" sounds either uneducated or dialectal. American English speakers may have a different take on it.

[Edit] Sorry, I forgot to mention that "I was never bitten by a shark" is the "fully correct" (not abbreviated) form if you're talking about a period that lies wholly in the past (rather than the period up to the present). For example:

"I worked as an underwater cameraman for five years and I was never bitten by a shark."